# Thread: 1,1,1,1 Matrix general formula!!!

1. hmm are you sure?

when i did (X+Y)^2, i got
l4 0l
l0 4l

and i thought maybe A^n would be something like
l2^n-1 0l
l0 2^n-1l

that would work for all constants right?

2. Originally Posted by daRitz
hmm are you sure?

when i did (X+Y)^2, i got
l4 0l
l0 4l
No.You have computed it wrongly then
First of all, X+Y = I
And $\displaystyle I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$

Try computing $\displaystyle I^n$ and tell me what you get...

Originally Posted by daRitz
and i thought maybe A^n would be something like
l2^n-1 0l
l0 2^n-1l

that would work for all constants right?
$\displaystyle A = aX = \begin{pmatrix} a & a \\ a & a \end{pmatrix}$
Try computing $\displaystyle A^2, A^3$ and see....

3. Ok thanks i understand that one now!

Back to that previous problem,
A=aX, B=bX
you're formula was really good but i dont think that's what is supposed to be done because i didn't type the whole instructions:

Let A=aX and B=bX, where a and b are constants. use different velues of a and b to calculate A^2, A^3, A^4....(for references)

By considering integer powers of A and B, find expressions for A^n and B^n.

i honestly have no idea what they're asking in this problem, any idea?

4. Originally Posted by daRitz

Let A=aX and B=bX, where a and b are constants. use different velues of a and b to calculate A^2, A^3, A^4....(for references)

By considering integer powers of A and B, find expressions for A^n and B^n.

i honestly have no idea what they're asking in this problem, any idea?

"use different velues of a and b to calculate A^2, A^3, A^4....(for references)"

I am not sure what this means...

Probably your teacher wants you to guess the general formula for $\displaystyle A^n = (aX)^n$, by first trying some values.
Like you can try a=1, a=0 and a=2 and so on....

This will let you see a general pattern.... Then you guess that for a particular "a",

$\displaystyle A^n = \begin{pmatrix} a^n2^{n-1} & a^n2^{n-1} \\ a^n2^{n-1} & a^n2^{n-1} \end{pmatrix}$

Finally you should prove this guess using induction.......

5. ok, well tomorrow i'll ask her before class just to be sure this is what she wants.
thanks sooo much for your help!

6. Originally Posted by daRitz
ok, well tomorrow i'll ask her before class just to be sure this is what she wants.
thanks sooo much for your help!
You are welcome
Do tell me tomorrow what she wanted. I am curious about it

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